Embibe Experts Solutions for Chapter: Laws of Motion, Exercise 1: Exercise - 1

A box is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time $t$, it decelerates. Then the resultant contact force $R$ by the floor on the box is given best by:

A plank of mass $m_1=8 \mathrm{kg}$ with a bar of mass $m_2=2 \mathrm{kg}$ placed on its rough surface, lie on a smooth floor of elevator ascending with an acceleration $g/4$. The coefficient of friction is $\mu =1/5$ between $m_1$ and $m_2$. A horizontal force $F=30 \mathrm{N}$ is applied to the plank. Then the acceleration of bar and the plank in the reference frame of elevator are:

A steel ball of mass $0.5 \mathrm{kg}$ is dropped from a height of $4 \mathrm{m}$ on to a horizontal heavy steel slab. The ball strike the slab and rebounds to its original height. $\left(\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

(a) Calculate the impulse delivered to the ball during impact.

(b) If the ball is in contact with the slab for $0.002 \mathrm{s},$ find the average reaction force on the ball during impact.

A triangular block of mass $M$ rests on a smooth surface as shown in figure. A cubical block of mass $m$ rests on the inclined surface. If all surfaces are frictionless, the force that must be applied to $M$ so as to keep $m$ stationary relative to $M$ is

A block of mass $m$ resting on a wedge of angle $\theta$ as shown in the figure. The wedge is given an acceleration a towards left. What is the minimum value of $a$ due to external agent so that the mass $m$ falls freely?

The moment of inertia of the pulley system as shown in the figure is$3 \mathrm{kg} – {\mathrm{m}}^2 .$ The radii of bigger and smaller pulleys are $2\mathrm{m} \mathrm{and} 1\mathrm{m}$respectively. As the system is released from rest, find the angular acceleration of the pulley system. (Assume that there is no slipping between string & pulley and string is light) $[\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2} ]$

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is $T$. If the spring is divided into two equal parts and one part is used to continue the simple harmonic motion, the time period will,

Four massless springs whose force constants are $2k\text{,} 2k\text{,} k \text{and} 2k$, respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction, then the frequency of the system,